Problem 10 A time series of 100 monthly observations was recorded and a time series analysis was conducted. The following ARMA(2,1) model has been fit to the time series, {y}: y₁ = ₁₁-₁+ ₂y₁-2+ a₁0₁a-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution to the model has been obtained as: y = 0.6y-1 - 0.5y-2 + a +0.9a-1. Answer the following questions by considering the first and the last five values of the time series, {y}. t 96 97 98 1 2 3 4 5 20 26 25 31 34 99 100 32 yt 27 34 29 28 a. Calculate the first four point estimates of {v}, i.e., ŷ1, ŷ2, ŷ3, and ŷ4. b. Given â100=20, calculate the forecast for future period 101 at time t = 100, i.e., 101 - ...
Problem 10 A time series of 100 monthly observations was recorded and a time series analysis was conducted. The following ARMA(2,1) model has been fit to the time series, {y}: y₁ = ₁₁-₁+ ₂y₁-2+ a₁0₁a-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution to the model has been obtained as: y = 0.6y-1 - 0.5y-2 + a +0.9a-1. Answer the following questions by considering the first and the last five values of the time series, {y}. t 96 97 98 1 2 3 4 5 20 26 25 31 34 99 100 32 yt 27 34 29 28 a. Calculate the first four point estimates of {v}, i.e., ŷ1, ŷ2, ŷ3, and ŷ4. b. Given â100=20, calculate the forecast for future period 101 at time t = 100, i.e., 101 - ...
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Problem 10
A time series of 100 monthly observations was recorded and a time series analysis was
conducted. The following ARMA(2,1) model has been fit to the time series, {y}:
y₁ = ₁₁-1+ ₂Y₁-2+ a₁-0₁a₁-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution
to the model has been obtained as: y = 0.6y-1 - 0.5yt-2 +at+0.9a-1. Answer the following
questions by considering the first and the last five values of the time series, {y₁}.
t
1 2 3 4 5
96
97 98 99
100
Yt
20 26 25 31 34
27
34 29 28 32
a. Calculate the first four point estimates of {y}, i.e., ₁, 92, 93, and ŷ4.
b. Given â 100=20, calculate the forecast for future period 101 at time t = 100, i.e., ŷ101.
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